## Elementary Differential Equations and Boundary Value Problems 9th Edition

$(0,\infty)$
$y''+cos(t)y'+3ln|t|y=0$ To use Theorem 3.2.1: $p(t)=cos(t)$ which is continuous on $(-\infty,\infty)$ $q(t)=3ln|t|$ which is continuous on $(0,\infty)$ $g(t)=0$ which is continuous on $(-\infty,\infty)$ Thus, $p(t),q(t),$ and $g(t)$ are all continuous on $(0,\infty)$ Since $t_0=2$, the solution exists on $(0,\infty)$